Subgroups — C₇×#21490 #13198706

Order 1792.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
6	C₇×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#121	C₄	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
25	C₇×#436	—	2	4	no	—
26	C₇×#435	—	2	4	no	—
27	C₇×#435	—	2	4	no	—
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₇×M₁₆	—	2	4	no	—
41	C₂×C₇×#97	C₂²	1	1	yes	characteristic
42	C₂×C₇×#97	C₂²	1	1	yes	characteristic
43	C₂×C₇×#97	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
47	C₇×#390	C₄	1	1	yes	characteristic
48	C₇×#389	C₄	1	1	yes	characteristic
49	C₇×#388	C₄	1	1	yes	characteristic
50	C₇×#388	C₄	1	1	yes	characteristic
51	C₇×#386	C₄	1	1	yes	characteristic
52	C₇×#386	C₄	1	1	yes	characteristic
53	C₇×#380	C₄	1	1	yes	characteristic
54	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	C₇×#336	C₂²	1	1	yes	characteristic
63	#21490	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂×C₇×M₁₆	—	2	2	no	—
73	C₂×C₇×M₁₆	—	2	2	no	—
74	C₂×C₇×M₁₆	—	2	2	no	—
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	2	2	no	—
77	C₂×C₇×M₁₆	—	2	2	no	—
78	C₂×C₇×M₁₆	—	2	2	no	—
79	C₂×C₇×M₁₆	—	2	2	no	—
80	C₂×C₇×M₁₆	D₄	1	4	yes	complemented
81	C₂²×C₇×C₈	—	2	2	no	—
82	C₂²×C₇×C₈	—	2	2	no	—
83	C₂²×C₇×C₈	—	2	2	no	—
84	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₇×#121	—	2	4	no	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	—	2	2	no	—
95	C₄×C₇×D₄	—	2	2	no	—
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₄×C₇×D₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₇	—	2	2	no	—
115	C₂×C₄²×C₇	—	2	2	no	—
116	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊C₈	—	2	2	no	—
123	C₇×C₄⋊C₈	—	2	2	no	—
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×C₂²⋊C₈	—	2	2	no	—
127	C₇×C₂²⋊C₈	—	2	2	no	—
128	C₇×C₂²⋊C₈	—	2	2	no	—
129	C₇×C₂²⋊C₈	—	2	2	no	—
130	C₇×C₂²⋊C₈	—	2	2	no	—
131	C₇×C₂²⋊C₈	—	2	2	no	—
132	C₇×C₂²⋊C₈	—	2	2	no	—
133	C₇×C₂²⋊C₈	—	2	2	no	—
134	C₇×#97	—	2	2	no	—
135	C₇×#97	—	2	2	no	—
136	C₇×#97	D₄	1	4	yes	complemented
137	C₄×C₇×C₈	—	2	2	no	—
138	C₄×C₇×C₈	—	2	2	no	—
139	C₄×C₇×C₈	—	2	2	no	—
140	C₇×#95	C₂×C₄	1	1	yes	characteristic
141	C₇×#95	C₂×C₄	1	1	yes	characteristic
142	C₇×#95	C₂×C₄	1	1	yes	characteristic
143	C₇×#95	C₂×C₄	1	1	yes	characteristic
144	C₇×#95	C₂×C₄	1	1	yes	characteristic
145	C₇×#95	C₂×C₄	1	1	yes	characteristic
146	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
149	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
150	C₄×#121	C₂×C₇	1	1	yes	characteristic
151	#1955	C₂×C₇	1	1	yes	characteristic, complemented
152	#1940	C₂×C₇	1	1	yes	characteristic, complemented
153	#1923	C₂×C₇	1	1	yes	characteristic, complemented
154	#1923	C₂×C₇	1	1	yes	characteristic, complemented
155	#1870	C₂×C₇	1	1	yes	characteristic, complemented
156	#1870	C₂×C₇	1	1	yes	characteristic, complemented
157	#1797	C₂×C₇	1	1	yes	characteristic, complemented
158	#1771	C₂×C₇	1	1	yes	characteristic, complemented
159	#1753	C₂×C₇	1	1	yes	characteristic, complemented
160	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
161	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₇×D₄	—	2	2	no	—
165	C₂×C₇×D₄	—	2	2	no	—
166	C₂×C₇×D₄	—	2	2	no	—
167	C₂×C₇×D₄	—	2	2	no	—
168	C₂×C₇×D₄	—	2	2	no	—
169	C₂×C₇×D₄	—	2	2	no	—
170	C₂×C₇×D₄	—	4	1	no	—
171	C₂×C₇×D₄	—	4	1	no	—
172	C₂×C₇×D₄	—	4	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	2	no	—
179	C₂²×C₄×C₇	—	2	2	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	4	1	no	—
194	C₂²×C₄×C₇	—	4	1	no	—
195	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₇	#41	1	2	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
209	C₇×M₁₆	—	2	8	no	—
210	C₇×M₁₆	—	2	8	no	—
211	C₇×M₁₆	—	4	4	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	—	2	1	no	—
220	C₂×C₇×C₈	—	2	1	no	—
221	C₂×C₇×C₈	—	2	1	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	—	4	4	no	—
231	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
232	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
233	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
234	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
235	C₂×C₇×C₈	#41	1	2	yes	—
236	C₂×C₇×C₈	#41	1	2	yes	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	2	no	—
240	C₇×C₄⋊C₄	—	2	2	no	—
241	C₇×C₄⋊C₄	—	4	1	no	—
242	C₇×C₂²⋊C₄	—	2	2	no	—
243	C₇×C₂²⋊C₄	—	2	2	no	—
244	C₇×C₂²⋊C₄	—	2	2	no	—
245	C₇×C₂²⋊C₄	—	2	2	no	—
246	C₇×C₂²⋊C₄	—	2	2	no	—
247	C₇×C₂²⋊C₄	—	2	2	no	—
248	C₇×C₂²⋊C₄	—	2	2	no	—
249	C₇×C₂²⋊C₄	—	2	2	no	—
250	C₇×C₂²⋊C₄	—	2	2	no	—
251	C₇×C₂²⋊C₄	M₁₆	1	4	yes	complemented
252	C₄²×C₇	—	2	2	no	—
253	C₄²×C₇	—	2	2	no	—
254	C₄²×C₇	—	2	1	no	—
255	C₄²×C₇	—	2	1	no	—
256	C₄²×C₇	—	2	1	no	—
257	C₄²×C₇	—	2	1	no	—
258	C₄²×C₇	—	2	1	no	—
259	C₄²×C₇	—	2	1	no	—
260	C₄²×C₇	C₂×D₄	1	2	yes	—
261	C₄²×C₇	#41	1	2	yes	—
262	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×#121	C₄×C₇	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
270	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
271	#436	—	2	4	no	—
272	#435	—	2	4	no	—
273	#435	—	2	4	no	—
274	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
286	C₄×M₁₆	—	2	4	no	—
287	C₂×#97	C₂²×C₇	1	1	yes	characteristic
288	C₂×#97	C₂²×C₇	1	1	yes	characteristic
289	C₂×#97	C₂²×C₇	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
293	#390	C₄×C₇	1	1	yes	characteristic
294	#389	C₄×C₇	1	1	yes	characteristic
295	#388	C₄×C₇	1	1	yes	characteristic
296	#388	C₄×C₇	1	1	yes	characteristic
297	#386	C₄×C₇	1	1	yes	characteristic
298	#386	C₄×C₇	1	1	yes	characteristic
299	#380	C₄×C₇	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
303	#336	C₂²×C₇	1	1	yes	characteristic
304	#336	C₂²×C₇	1	1	yes	characteristic
305	#336	C₂²×C₇	1	1	yes	characteristic
306	#336	C₂²×C₇	1	1	yes	characteristic
307	#336	C₂²×C₇	1	1	yes	characteristic
308	#336	C₂²×C₇	1	1	yes	characteristic
309	C₂³×C₇	—	2	1	no	—
310	C₂³×C₇	—	2	1	no	—
311	C₂³×C₇	—	2	1	no	—
312	C₂³×C₇	—	2	1	no	—
313	C₂³×C₇	—	2	1	no	—
314	C₂³×C₇	—	2	1	no	—
315	C₂³×C₇	—	2	1	no	—
316	C₂³×C₇	—	2	1	no	—
317	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	2	1	no	—
321	C₂³×C₇	—	2	1	no	—
322	C₂³×C₇	—	2	1	no	—
323	C₂³×C₇	—	2	1	no	—
324	C₂³×C₇	—	2	1	no	—
325	C₂³×C₇	—	2	1	no	—
326	C₂³×C₇	—	2	1	no	—
327	C₂³×C₇	—	2	1	no	—
328	C₂³×C₇	C₄×D₄	1	2	yes	—
329	C₂³×C₇	C₂×M₁₆	1	2	yes	—
330	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
331	C₇×D₄	—	4	4	no	—
332	C₇×D₄	—	4	4	no	—
333	C₇×D₄	—	4	4	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	2	1	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	2	1	no	—
364	C₂×C₄×C₇	—	2	1	no	—
365	C₂×C₄×C₇	—	4	4	no	—
366	C₂×C₄×C₇	—	4	4	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	1	no	—
371	C₂×C₄×C₇	—	4	1	no	—
372	C₂×C₄×C₇	—	4	1	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	1	no	—
375	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
376	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
377	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
378	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
379	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
380	C₂×C₄×C₇	#131	1	2	yes	—
381	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
386	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
387	C₇×C₈	—	2	2	no	—
388	C₇×C₈	—	2	2	no	—
389	C₇×C₈	—	2	2	no	—
390	C₇×C₈	—	4	1	no	—
391	C₇×C₈	—	4	1	no	—
392	C₇×C₈	—	4	1	no	—
393	C₇×C₈	—	4	1	no	—
394	C₇×C₈	#121	1	4	yes	complemented
395	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
396	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
397	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
398	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
399	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂×M₁₆	—	2	2	no	—
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	—	2	2	no	—
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂×M₁₆	—	2	2	no	—
409	C₂×M₁₆	—	2	2	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	C₇×D₄	1	4	yes	complemented
412	C₂²×C₈	—	2	2	no	—
413	C₂²×C₈	—	2	2	no	—
414	C₂²×C₈	—	2	2	no	—
415	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
423	#121	—	2	4	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
445	C₂×C₄²	—	2	2	no	—
446	C₂×C₄²	—	2	2	no	—
447	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
448	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
453	C₄⋊C₈	—	2	2	no	—
454	C₄⋊C₈	—	2	2	no	—
455	C₄⋊C₈	—	2	2	no	—
456	C₄⋊C₈	—	2	2	no	—
457	C₂²⋊C₈	—	2	2	no	—
458	C₂²⋊C₈	—	2	2	no	—
459	C₂²⋊C₈	—	2	2	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	—	2	2	no	—
462	C₂²⋊C₈	—	2	2	no	—
463	C₂²⋊C₈	—	2	2	no	—
464	C₂²⋊C₈	—	2	2	no	—
465	#97	—	2	2	no	—
466	#97	—	2	2	no	—
467	#97	C₇×D₄	1	4	yes	complemented
468	C₄×C₈	—	2	2	no	—
469	C₄×C₈	—	2	2	no	—
470	C₄×C₈	—	2	2	no	—
471	#95	C₂×C₄×C₇	1	1	yes	characteristic
472	#95	C₂×C₄×C₇	1	1	yes	characteristic
473	#95	C₂×C₄×C₇	1	1	yes	characteristic
474	#95	C₂×C₄×C₇	1	1	yes	characteristic
475	#95	C₂×C₄×C₇	1	1	yes	characteristic
476	#95	C₂×C₄×C₇	1	1	yes	characteristic
477	C₂²×C₇	—	2	2	no	—
478	C₂²×C₇	—	2	2	no	—
479	C₂²×C₇	—	2	2	no	—
480	C₂²×C₇	—	2	2	no	—
481	C₂²×C₇	—	2	2	no	—
482	C₂²×C₇	—	2	2	no	—
483	C₂²×C₇	—	4	1	no	—
484	C₂²×C₇	—	4	1	no	—
485	C₂²×C₇	—	4	1	no	—
486	C₂²×C₇	—	4	1	no	—
487	C₂²×C₇	—	4	1	no	—
488	C₂²×C₇	—	4	1	no	—
489	C₂²×C₇	—	4	1	no	—
490	C₂²×C₇	—	4	1	no	—
491	C₂²×C₇	—	4	1	no	—
492	C₂²×C₇	—	4	1	no	—
493	C₂²×C₇	—	4	1	no	—
494	C₂²×C₇	—	4	1	no	—
495	C₂²×C₇	—	4	1	no	—
496	C₂²×C₇	—	4	1	no	—
497	C₂²×C₇	—	4	1	no	—
498	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
499	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
500	C₂²×C₇	C₄×#41	1	1	yes	characteristic
501	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
502	C₂²×C₇	C₂×#131	1	1	yes	characteristic
503	C₂²×C₇	#568	1	1	yes	characteristic
504	C₂²×C₇	#568	1	1	yes	characteristic
505	C₄×C₇	—	2	2	no	—
506	C₄×C₇	—	2	2	no	—
507	C₄×C₇	—	2	2	no	—
508	C₄×C₇	—	2	2	no	—
509	C₄×C₇	—	2	2	no	—
510	C₄×C₇	—	2	2	no	—
511	C₄×C₇	—	4	1	no	—
512	C₄×C₇	—	4	1	no	—
513	C₄×C₇	—	4	1	no	—
514	C₄×C₇	—	4	1	no	—
515	C₄×C₇	—	4	1	no	—
516	C₄×C₇	C₂×#121	1	1	yes	characteristic
517	C₄×C₇	#525	1	1	yes	characteristic
518	C₄×C₇	#529	1	1	yes	characteristic
519	C₄×C₇	#532	1	1	yes	characteristic
520	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
521	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
522	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
557	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
562	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
565	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
566	C₂²×C₄	C₇×#41	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
568	M₁₆	—	2	8	no	—
569	M₁₆	—	2	8	no	—
570	M₁₆	—	4	4	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	4	4	no	—
590	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
591	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
592	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
593	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
594	C₂×C₈	C₇×#41	1	2	yes	—
595	C₂×C₈	C₇×#41	1	2	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	C₇×M₁₆	1	4	yes	complemented
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	C₂×C₇×D₄	1	2	yes	—
620	C₄²	C₇×#41	1	2	yes	—
621	C₂×C₇	—	4	2	no	—
622	C₂×C₇	—	4	2	no	—
623	C₂×C₇	—	8	1	no	—
624	C₂×C₇	C₄×#121	1	1	yes	characteristic
625	C₂×C₇	#2933	1	1	yes	characteristic
626	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
627	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
628	C₂×C₇	#2935	1	1	yes	characteristic
629	C₂×C₇	#2965	1	1	yes	characteristic
630	C₂×C₇	#2967	1	1	yes	characteristic
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	C₄×C₇×D₄	1	2	yes	—
651	C₂³	C₂×C₇×M₁₆	1	2	yes	—
652	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
653	D₄	—	4	4	no	—
654	D₄	—	4	4	no	—
655	D₄	—	4	4	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
698	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
699	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
700	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
701	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
702	C₂×C₄	C₇×#131	1	2	yes	—
703	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
706	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
707	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
708	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
709	C₈	—	2	2	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	4	1	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	C₇×#121	1	4	yes	complemented
717	C₇	#21490	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
740	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
741	C₂²	C₄×C₇×#41	1	1	yes	characteristic
742	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
743	C₂²	C₂×C₇×#131	1	1	yes	characteristic
744	C₂²	C₇×#568	1	1	yes	characteristic
745	C₂²	C₇×#568	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	C₂×C₇×#121	1	1	yes	characteristic
758	C₄	C₇×#525	1	1	yes	characteristic
759	C₄	C₇×#529	1	1	yes	characteristic
760	C₄	C₇×#532	1	1	yes	characteristic
761	C₂	—	4	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	1	no	—
764	C₂	C₄×C₇×#121	1	1	yes	characteristic
765	C₂	C₇×#2933	1	1	yes	characteristic
766	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
767	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
768	C₂	C₇×#2935	1	1	yes	characteristic
769	C₂	C₇×#2965	1	1	yes	characteristic
770	C₂	C₇×#2967	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#436	C₂	semidirect
2. C₂×C₇×#435	C₂	semidirect
3. C₂×C₇×#435	C₂	semidirect
4. C₂×C₄×C₇×M₁₆	C₂	semidirect
6. C₇×#1955	C₂	semidirect
7. C₇×#1940	C₂	semidirect
8. C₇×#1923	C₂	semidirect
9. C₇×#1923	C₂	semidirect
10. C₇×#1870	C₂	semidirect
11. C₇×#1870	C₂	semidirect
12. C₇×#1797	C₂	semidirect
13. C₇×#1771	C₂	semidirect
14. C₇×#1753	C₂	semidirect
15. C₇×C₈×C₂²⋊C₄	C₂	semidirect
63. #21490	C₇	direct (N × H)
80. C₂×C₇×M₁₆	D₄	semidirect
136. C₇×#97	D₄	semidirect
146. C₂×#436	C₂×C₇	semidirect
147. C₂×#435	C₂×C₇	semidirect
148. C₂×#435	C₂×C₇	semidirect
149. C₂×C₄×M₁₆	C₂×C₇	semidirect
151. #1955	C₂×C₇	semidirect
152. #1940	C₂×C₇	semidirect
153. #1923	C₂×C₇	semidirect
154. #1923	C₂×C₇	semidirect
155. #1870	C₂×C₇	semidirect
156. #1870	C₂×C₇	semidirect
157. #1797	C₂×C₇	semidirect
158. #1771	C₂×C₇	semidirect
159. #1753	C₂×C₇	semidirect
160. C₈×C₂²⋊C₄	C₂×C₇	semidirect
251. C₇×C₂²⋊C₄	M₁₆	semidirect
394. C₇×C₈	#121	semidirect
411. C₂×M₁₆	C₇×D₄	semidirect
467. #97	C₇×D₄	semidirect
610. C₂²⋊C₄	C₇×M₁₆	semidirect
716. C₈	C₇×#121	semidirect
717. C₇	#21490	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₄×C₇×M₁₆	2
C₄×C₇×#121	2
C₇×#1955	2
C₇×#1940	2
C₇×#1923	2
C₇×#1870	2
C₇×#1797	2
C₇×#1771	2
C₇×#1753	2
C₇×C₈×C₂²⋊C₄	2
#21490	7

Subgroups — C7×#21490 #13198706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21490 #13198706